Rocket with constant acceleration for 16s reaching 5100m at 20s

[Slacker142]

So this problem is giving me some issues, my algebra may be rusty so it has me stumped.

A Rocket experiences constant acceleration upward for 16s and then stops accelerating. It continues upward and at time 20s the distance from the ground is 5100 meters. Find the acceleration experienced during the 16s. What is the rockets speed as it passes a cloud at 5100m.


The best I could do was get the equation 5100-x = .5a*16²

Where a is the acceleration during the 16s and 5100-x is equal to the distance traveled during that time.

all this coming from the basic equation S_f=S₀+V₀t+.5at²

This leads me to think i should use a system of equations to solve it but I am really stumped as how to begin


Any suggestions would be helpful, I'd really like to solve it on my own though so no solutions please

 

[rl.bhat]

Time 20 second is from the beginning or after 16 seconds?

 

[Slacker142]

Time 20 second is from the beginning or after 16 seconds?

from the beginning so 4 seconds after the rocket stops

 

[Slacker142]

Nevermind, figured it out

 

[rl.bhat]

If x is the distance traveled in 4 seconds, then
x = vf*4 - 0.5*g*16...(1)
vf = vi + 16*a...(2) Here vi = 0.
So x = 64*a - 8*g...(3)
You have already written
5100 - x = 0.5*a*16^2...(4)
Substitute the value of x and solve for a.